Dani is a distinctive girls' name in England & Wales, ranking #809 in 2002 with 30 recorded births. The name reached its all-time peak in 1996 with 43 births ranking #571. Since 1996, the popularity has decreased by 30.2%. In 2002, approximately 1 in every 8,912 girls born was named Dani. FALLING Recent data shows the name is currently falling.